Internet Protocol flows present high variability at small time scales as well as long range dependence, which can be captured by multifractal models. Estimating the bandwidth to support the Quality of Service required by these flows is the key to Traffic Engineering. This paper introduces a novel envelope process which is a minimalist yet accurate model for multifractal flows. The envelope process is an upper bound to the volume of arrivals from a multifractal Brownian motion. The envelope process accuracy was assessed using both real network traces and synthetically generated traces. Moreover, the solution of a queue fed by multifractal flows is presented and an expression for the time at which the queue length reaches its maximum is derived. This time instant is used for the derivation of an efficient method for the computation of the equivalent bandwidth of multifractal flows. Furthermore, a policing mechanisms to assure the conformance of a flow to the multifractal envelope process is presented. It is also shown that a monofractal approach for modeling multifractal flows leads to overestimation of the bandwidth needed. © 2005 Elsevier B.V. All rights reserved.483351375